Abstract. We introduce a simple algorithm to improve existing density surfaces to ensure that the resulting surfaces are as close to neutral as possible. This means the slopes at any point on the surfaces are close to neutral tangent planes – the directions along which layered stirring and mixing occurs – minimizing the fictitious diapycnal diffusivity. Inverse techniques and layered models have been used for decades to understand ocean circulation. The most-used density surfaces are potential density or neutral density surfaces. Both these density surfaces and all others produce a fictitious diapycnal diffusivity to some degree due to the helical nature of neutral trajectories – with the magnitude of this artificial diffusivity in some cases being larger than the values measured in the ocean. Here we show how this error can be reduced by up to four orders of magnitude and therefore becomes insignificant compared to measured values, thus providing surfaces which would produce more accurate results when used for inverse techniques.